The Gergonne point generalized through convex coordinates - J. N. Boyd; P. N. Raychowdhury (International Journal of Mathematics and Mathematical Sciences)
The Gergonne point of a triangle is the point at which the three cevians to the points of tangency between the incircle and the sides of the triangle are concurrent. In this paper, we follow Koneĉný [7] in generalizing the idea of the Gergonne point and find the convex coordinates of the generalized Gergonne point. We relate these convex coordinates to the convex coordinates of several other special points of the triangle. We also give an example of relevant computations.